9514 1404 393
Answer:
|m-2.5| ≤ 0.08
2.42 ≤ m ≤ 2.58
Step-by-step explanation:
The equation of interest is the one that says the positive difference from the ideal mass is at most 0.08 ounces:
|m -2.5| ≤ 0.08 . . . an absolute value inequality
The solution is found by solving the equivalent compound inequality:
-0.08 ≤ m -2.5 ≤ 0.08
2.42 ≤ m ≤ 2.58 . . . . the range of masses
what is the solution of x=2+ sqrt x-2
Answer:
C
Step-by-step explanation:
[tex]x=2+\sqrt{x-2} \\\\x-2=\sqrt{x-2} \\\\(x-2)^2=\pm(x-2) \\\\x^2-4x+4=\pm(x-2) \\\\[/tex]
[tex]x^2-5x+6=0[/tex] OR [tex]x^2+3x+2=0[/tex]
x=2 and 3
Hope this helps!
Answer:
The answer is option 3.
Step-by-step explanation:
Firstly, we have to move the unrelated term to the other side :
[tex]x = 2 + \sqrt{x - 2} [/tex]
[tex]x - 2 = \sqrt{x - 2} [/tex]
Then, you have to get rid of square root by squaring both sides :
[tex] {(x - 2)}^{2} = {( \sqrt{x - 2} )}^{2} [/tex]
[tex] {x}^{2} - 4x + 2 = x - 2[/tex]
[tex] {x}^{2} - 4x + 4 - x + 2 = 0[/tex]
[tex] {x}^{2} - 5x + 6 = 0[/tex]
Next, you have to solve it :
[tex] {x}^{2} - 5x + 6 = 0[/tex]
[tex] {x}^{2} - 2x - 3x + 6 = 0[/tex]
[tex]x(x - 2) - 3(x - 2) = 0[/tex]
[tex](x - 2)(x - 3) = 0[/tex]
[tex]x - 2 = 0 \\ x = 2[/tex]
[tex]x - 3 = 0 \\ x = 3[/tex]
A team averaging 110 points is likely to do very well during the regular season. The coach of your team has hypothesized that your team scored at an average of less than 110 points in the years 2013-2015. Test this claim at a 1% level of significance. For this test, assume that the population standard deviation for relative skill level is unknown.
Answer:
There is not enough evidence to support the claim that your team scored an average significantly less than 110 points.
Step-by-step explanation:
The question is incomplete:
There is no data from the sample.
We will use the sample [105 107 117 106 110 ] as an example to solve the question.
The mean of the sample is:
[tex]M=\dfrac{1}{5}\sum_{i=1}^{5}(105+107+117+106+110)\\\\\\ M=\dfrac{545}{5}=109[/tex]
The standard deviation of the sample is:
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{5}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}\cdot [(105-(109))^2+(107-(109))^2+(117-(109))^2+(106-(109))^2+(110-(109))^2]}\\\\\\ s=\sqrt{\dfrac{1}{4}\cdot [(16)+(4)+(64)+(9)+(1)]}\\\\\\ s=\sqrt{\dfrac{94}{4}}=\sqrt{23.5}\\\\\\s=4.848[/tex]
This is a hypothesis test for the population mean.
The claim is that your team scored an average significantly less than 110 points.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=110\\\\H_a:\mu< 110[/tex]
The significance level is 0.01.
The sample has a size n=5.
The sample mean is M=109.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=4.848.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{4.848}{\sqrt{5}}=2.17[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{109-110}{2.17}=\dfrac{-1}{2.17}=-0.46[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=5-1=4[/tex]
This test is a left-tailed test, with 4 degrees of freedom and t=-0.46, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-0.46)=0.334[/tex]
As the P-value (0.334) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that your team scored an average significantly less than 110 points.
A book claims that more hockey players are born in January through March than in October through December. The following data show the number of players selected in a draft of new players for a hockey league according to their birth month. Is there evidence to suggest that hockey players' birthdates are not uniformly distributed throughout the year? Use the level of significance α= 0.05.
Birth Month Frequency
January-March 67
April-June 56
July-September 30
October-December 37
What are the null and alternative hypotheses?
Answer:
[tex]\chi^2 = \frac{(67-47.5)^2}{47.5}+\frac{(56-47.5)^2}{47.5}+\frac{(30-47.5)^2}{47.5}+\frac{(37-47.5)^2}{47.5}=18.295[/tex]
Now we can calculate the degrees of freedom for the statistic given by:
[tex]df=(categories-1)=4-1=3[/tex]
And we can calculate the p value given by:
[tex]p_v = P(\chi^2_{3} >18.295)=0.00038[/tex]
Since the p value is very low we have enough evidence to reject the null hypothesis and we can conclude that the players' birthdates are not uniformly distributed throughout the year
Step-by-step explanation:
We need to conduct a chi square test in order to check the following hypothesis:
H0: There is no difference of birthdates distributed throughout the year
H1: There is a difference between birthdates distributed throughout the year
The level of significance assumed for this case is [tex]\alpha=0.05[/tex]
The statistic to check the hypothesis is given by:
[tex]\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
The table given represent the observed values, we just need to calculate the expected values with the following formula [tex]E_i = \frac{total}{4}[/tex]
And replacing we got:
[tex]E_{1} =\frac{67+56+30+37}{4}=47.5[/tex]
And now we can calculate the statistic:
[tex]\chi^2 = \frac{(67-47.5)^2}{47.5}+\frac{(56-47.5)^2}{47.5}+\frac{(30-47.5)^2}{47.5}+\frac{(37-47.5)^2}{47.5}=18.295[/tex]
Now we can calculate the degrees of freedom for the statistic given by:
[tex]df=(categories-1)=4-1=3[/tex]
And we can calculate the p value given by:
[tex]p_v = P(\chi^2_{3} >18.295)=0.00038[/tex]
Since the p value is very low we have enough evidence to reject the null hypothesis and we can conclude that the players' birthdates are not uniformly distributed throughout the year
PLZ HURRRY!!!!! What is the circumference of the circle
Answer:
40.192
Step-by-step explanation:
C=D(pi)
D=6.2*2
C=12.8*3.12
C=40.192
Answer:40.192
Step-by-step explanation:the formula for a circumference if a circle is C=2•3.14•r^2 fill in for r and calculate for your answer
An aquarium holds 11.08 cubic feet of water,and is 2.5 feet long 1.3 feet wide.what is its depth.Round your answer to the nearest whole number.
Answer:
3ft
Step-by-step explanation:
volume = l*w*h
To solve use what you know.
11.08 ft^3 = 2.5 ft * 1.3 ft * X ft
2.5 ft *1.3 ft =3.5 ft^2
11.08ft^3 / 3.5ft^2 = 3.409 ft
nearest whole number is 3 ft
State whether the data described below are discrete or continuous, and explain why. The exact mass (in grams )of food eaten by a person each day nothing Choose the correct answer below. A. The data are continuous because the data can take on any value in an interval. B. The data are continuous because the data can only take on specific values. C. The data are discrete because the data can take on any value in an interval. D. The data are discrete because the data can only take on specific values
Answer:
A. The data are continuous because the data can take on any value in an interval.
Step-by-step explanation:
The data surveyed is the exact mass, in grams, of food eaten by each person each day.
This type of data is continous, not discrete. The mass can take any value within the domain of positive real numbers. It represents a physic variable, and they are always continous.
Which undefined term is used to define an angle?
O line
O plane
opoint
O ray
Answer:
A point would be used as the undefined term
A farmer has a total of 21 cows and chickens altogether The animals have 54 legs how many cows and how many chickens does the farmer have?
Answer:
The farmer has 4 cows and 15 chickens.
Step-by-step explanation:
This question can be solved using a system of equations.
I am going to say that:
x is the number of cows
y is the number of chickens.
A farmer has a total of 21 cows and chickens altogether
This means that x + y = 21.
The animals have 54 legs
A cow has four legs, while a chicken has 2 legs. So
4x + 2y = 54.
From the first equation:
y = 21 - x
Replacing
4x + 2(21 - x) = 54
4x + 42 - 2x = 54
2x = 12
x = 6
y = 21 - x = 21 - 6 = 15
The farmer has 4 cows and 15 chickens.
The number of customers in a line at a supermarket express checkout counter is a random variable with the following probability distribution. x 0 1 2 3 4 5 P(x) 0.09 0.26 0.29 0.20 0.09 0.07 Find P(2 or fewer).
Answer:
probability (x ≤2) = 0.64
Step-by-step explanation:
P(2 or fewer) = probability of 2 or fewer
probability of (2 or fewer) = probability (x ≤2)
probability of (2 or fewer) = probability when x is 0 + probability when x is 1 + probability when x is 2
probability of (2 or fewer) = probability (x =0) + probability of (x =1 ) + probability (x= 2)
probability of (x=0) = 0.09
probability of (x=1) = 0.26
probability of (x =2) = 0.29
probability of (2 or fewer) = 0.09 + 0.26 + 0.29 = 0.64
probability (2 or fewer) = probability (x ≤2) = 0.64
Answer:
[tex] P(X \leq 2)= P(X=0) +P(X=1)+P(X=2)[/tex]
And replacing we got:
[tex] P(X \leq 2)= 0.09 +0.26+0.29 = 0.64[/tex]
And the probability that X would be 2 or lower is 0.64
Step-by-step explanation:
For this case we have the following probability distribution:
x 0 1 2 3 4 5
P(x) 0.09 0.26 0.29 0.20 0.09 0.07
And we want to find the following probability:
[tex] P(X \leq 2)[/tex]
And we can find the probability like this:
[tex] P(X \leq 2)= P(X=0) +P(X=1)+P(X=2)[/tex]
And replacing we got:
[tex] P(X \leq 2)= 0.09 +0.26+0.29 = 0.64[/tex]
And the probability that X would be 2 or lower is 0.64
Any help would be great
What’s the correct answer for this?
Answer:
cats constitute the same fraction of animals adopted as not adopted
(i am actually not that sure)
Answer:
a
Step-by-step explanation:
as mamy cats as dogs are addopted
Sung Lee invests $5,000 at age 18. He hopes the investment will be worth $20,000 when he turns 25. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.
Answer:
19.8%
Step-by-step explanation:
We have the following formula for continuous compound interest:
A = P * e ^ (i * t)
Where:
A is the final value
P is the initial investment
i is the interest rate in decimal
t is time.
The time can be calculated as follows:
25 - 18 = 7
That is, the time corresponds to 7 years. In addition, A is 20,000 for A and P would be 5,000, we replace:
20000 = 5000 * e ^ (7 * i)
20000/5000 = e ^ (7 * i)
e ^ (7 * i) = 4
ln e ^ (7 * i) = ln 4
7 * i = ln 4
i = (ln 4) / 7
i = 0.198
Which means that the rounded percentage will be 19.8% per year
The rate of growth needed to achieve this goal is 22%
A compound interest is given by the formula:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
Where A is the final amount, r is the rate, t is the period, P is the principal and n is the number of times compounded in a period.
Given that A = 20000, P = 5000, t = 7 (25 - 18). hence:
[tex]20000=5000(1+\frac{r}{1} )^{7*1}\\\\4=(1+r )^{7}\\\\\\ln(4)=7\ ln(1+r)\\\\r=0.22[/tex]
Therefore the rate of growth needed to achieve this goal is 22%
Find out more at: https://brainly.com/question/22803385
what is a random variable
Answer:
Check Below.
Step-by-step explanation:
In Probability/ Statistics in simple terms it is a variable which possess the following characteristics within a sample space: 1) Their values are defined within the set of Real Numbers, i.e. it is a Quantitative variable. 2) It is possible to calculate its probability.
Exercise #1: The amount of money in Nicole's bank account can be represented by the function f(x) = 32.50x + 200,
where f(x) is the amount of money in dollars after x days. State the meaning of the slope and y-intercept of this function in
the given context
Matt and Chris leave their uncle's house in Phoenix at the same time. Matt drives west on I-60 at a speed of 76 miles per hour. Chris drives east on I-60 at a speed of 81 miles per hour. How many hours will it take them to be 785 miles apart?
Answer:
4 hours.
Step-by-step explanation:
A 3650-year-old wooden chest is found by archaeologists. What percentage of the original Superscript 14 Baseline Upper C would you expect to find in the wooden chest? (Recall that the decay constant for Superscript 14 Baseline Upper C is 0.00012.)
Answer:
64.5%
Step-by-step explanation:
Initial amount N° = ?
Remaining amount after decay = N = ?
k = decay constant = 0.00012 [tex]yr^{-1}[/tex]
t = time = 3650 year
fraction remaining will be N/N°
From the decay equation, N = N°[tex]e^{-kt}[/tex]
N/N° = [tex]e^{-kt}[/tex]
N/N° = [tex]e^{-0.00012 x 3650 }[/tex]
N/N° = [tex]e^{-0.438}[/tex]
N/N° = 0.645 = 64.5%
8 x 10^3 is how many times as large as 4 x 10^2?
8 * 10^3 is larger than 4 * 10^2
10*10*10 = 1000 * 8 = 8000
10*10= 100 * 4 = 400
A study by Consumer Reports showed that 64% of supermarket shoppers believesupermarket brands to be as good as national brands. A manager of a local storebelieves that the percentage is higher in his store. She asks a random sample of145 shoppers whether they believed that supermarket brand ketchup was as goodas the national brand ketchup. Out of the 145 shoppers asked, 89 believed the supermarket brand was as good as the national brand. Use α= 0.05 significancelevel and conduct a hypothesis test.
Answer:
[tex]z=\frac{0.614 -0.64}{\sqrt{\frac{0.64(1-0.64)}{145}}}=-0.652[/tex]
The p value would be given by:
[tex]p_v =P(z<-0.654)=0.257[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.64 at 5% of significance
Step-by-step explanation:
Information given
n=145 represent the random sample taken
X=89 represent the number of people who believed the supermarket brand was as good as the national brand
[tex]\hat p=\frac{89}{145}=0.614[/tex] estimated proportion of people who believed the supermarket brand was as good as the national brand
[tex]p_o=0.64[/tex] is the value to test
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true proportion is less than 0.64, the system of hypothesis are.:
Null hypothesis:[tex]p \geq 0.64[/tex]
Alternative hypothesis:[tex]p < 0.64[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{0.614 -0.64}{\sqrt{\frac{0.64(1-0.64)}{145}}}=-0.652[/tex]
The p value would be given by:
[tex]p_v =P(z<-0.654)=0.257[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is significantly less than 0.64 at 5% of significance
A builder makes drainpipes that drop 1 cm over a
horizontal distance of 30 cm to prevent clogs. See the
diagram below, which is not drawn to scale:
A certain drainpipe needs to cover a horizontal distance
of 700 cm
What is the length l of this drainpipe?
Round your answer to the nearest tenth of a centimeter
cm
Answer:
700.4 cm
Step-by-step explanation:
This involves two similar triangles.
Both triangles are right triangles.
One has legs measuring 1 cm and 30 cm. We can find the hypotenuse by using the Pythagorean theorem.
(1 cm)^2 + (30 cm)^2 = c^2
c^2 = 901 cm^2
c = sqrt(901) cm
The second triangle has one leg with length 700 cm. This leg corresponds to the 30-cm leg in the other triangle. Since the triangles are similar, we can use a proportion to find the hypotenuse of the second triangle.
(30 cm)/(700 cm) = [sqrt(901) cm]/x
3/70 = sqrt(901) cm/x
3x = 70 * sqrt(901) cm
x = 70 * sqrt(901) cm/3
x = 700.4 cm
Answer: 700.4 cm
The length of drainpipe is 700.4 cm.
What is Pythagoras theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
One has legs measuring 1 cm and 30 cm.
Using Pythagorean theorem.
(1 cm)² + (30 cm)² = c²
c² = 901
c =√901 cm
Since the triangles are similar, we can use a proportion to find the hypotenuse of the second triangle.
(30 cm)/(700 cm) = [√(901) cm]/x
3/70 = √(901) cm/x
3x = 70 x √(901) cm
x = 700.4 cm
Learn more about Pythagoras theorem here:
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#SPJ7
5)
Calculate the ratio to the nearest hundredth.
-
RATIO
U
DIAMETER (d) CIRCUMFERENCE (C)
20 in.
62.83 in.
är
liliom
DE
10 in.
31.41 in.
6
in.
18.84 in.
2
in.
6.28 in.
1
in.
3.14 in.
0
-
Complete
A
16% Complete
earch
'o
e
Answer:
Answer for (a) to (e) = 0.32
Calculate the ratio to the nearest hundredth.
Find the Ratio of Diameter (d) and circumference (C)
Step by step explanation:
In order to determine the ratio we must know the formula for the circumference of a circle. Then relate it to the diameter.
But since we have been the value if both circumference and diameter, we would just calculate the ratio.
Circumference of a circle = 2πr
Where d = diameter = 2r
Circumference = πd
a) d = 20 in.
C = 62.83 in.
Ratio of Diameter (d) and circumference (C) = d:C
= 20/(62.83)
d:C = 0.32
b) d=10 in.
C =31.41 in.
d:C = 10/(31.41)
d:C = 0.32
c) d =6 in.
C =18.84 in.
d:C = 6/(18.84)
d:C = 0.32
d) d= 2 in.
C = 6.28 in.
d:C = 2/6.28
d:C = 0.32
e) d = 1 in.
C = 3.14 in.
d:C = 1/3.14
d:C = 0.32
The above answers indicate that the ratio of a circumference of a circle to its diameter = d/C = d/(π×d)
= 1/π = 0.32
Evaluate this power with a base that is a negative fraction.
(−1
4
)2
Answer:
(16)^-1 or (4)^-2
Step-by-step explanation:
(-1/4)^2, we can convert this to (1/16), which is (16)^-1 or (4)^-2.
Answer:
[tex]\frac{1}{16}[/tex]
Step-by-step explanation:
[tex]-\frac{1}{4} ^{2}[/tex]
[tex]\frac{-1^{2} }{4^{2} }[/tex]
[tex]=\frac{1}{16}[/tex]
How many yards are in 108 inches?
Answer:
3 yards
Step-by-step explanation:
Divide inches by 36
[tex]108/36\\=3yards[/tex]
Answer:
[tex]3 \: \: yards[/tex]
Step-by-step explanation:
[tex]1 \: \: yard = 36\: \: inches \\ yard \: \: x = 108 \: \: inches[/tex]
So,
[tex] 1 = 36 \\ x = 108 \\ \\ cross \: \: \: multiple \\ \\ 108 = 36x \\ \frac{108}{36} = \frac{36x}{36} \\ x = 3 \: \: yards[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Find the mode of the following data:
18, 17, 12, 14, 8, 21, 10, 11, 19, 20, 10, 5, 17, 12, 10, 20
O A. 13
OB. 10
O c. 16
D. 14
SUBMIT
10..................
Three angles are given; Start with angle measures 80,40, and 60. try other sets of angles such as 20, 120, and 40. try three measures that dont add up to 180
Answer: 30, 60 and 80
Step-by-step explanation:
measures 80,40, and 60. And sets of angles such as 20, 120, and 40 will make two different triangles.
To try three measures that dont add up to 180 will never make a triangle.
One of them can be 30, 60, 80
here are 4 fracion labeled a b c d 3/4 5/6 16/25 9/15 order starting from smallest
Answer:
9/15
16/25
3/4
5/6
Step-by-step explanation:
Convert them to decimals then order them
Answer:
16/25, 9/15, 5/6, 3/4
Step-by-step explanation:
16/25
9/15
5/6
3/4
A probability model for rolling a cube with faces numbered 1 through 6 is:
Answer:
P(a)= Your desired outcome / The number of real outcomes.
Step-by-step explanation:
Ex. Probability model for rolling a 1 on a 6 sided die -
1 (desired outcome) / 6 (Number of real outcomes)
Let me know if you need more help!
the little boxes on the bottom with the numbers in it are the answers. plz do all three if u can
Answer:
is this correct? hope it works
Answer:
The difference of a number and 4 is 11
=> That number is 11 + 4 = 15
The quotient of a number and 13 is 78
=> The number is 13 x 78 = 1014
6.5 more than a number is 19.1
=> The number is 19.1 - 6.5 = 12.6
Hope this helps!
:)
A camp counselor and six campers are to be seated along a picnic bench. In how many ways could this be done if the counselor occupies the seat in the middle and the camper who tends to start food fights sits next to him (either on the left or on the right)
Answer:
This can be done in 240 ways.
Step-by-step explanation:
Number of arrangments:
The possible number of arrangments of n elements is given by the following formula:
[tex]A_{n} = n![/tex]
In this question:
7 people(camp counselor and six campers).
Camp counselor in the middle.
Camper who start food fights either to his left or to his right. For each of these cases, the other 5 campers are arranged in 5 positions. Then
How many ways:
[tex]T = 2A_{5} = 2*(5!) = 240[/tex]
This can be done in 240 ways.
Please Help, Math Problem.....
Answer:
Answer is given below with explanations.
Step-by-step explanation:
Given that triangle ABC is similar to triangle PQR
Then
Angle A is congruent to Angle PAngle B is congruent to Angle QAngle C is congruent to Angle RLine segment AB is congruent to Line segment PQLine segment BC is congruent to Line segment QRLine segment AC is congruent to Line segment PR .
THEN THE CORRECT OPTIONS ARE
OPTION D) AND
OPTION E)
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
When 893893 male workers were asked how many hours they worked in the previous week, the mean was 45.645.6 with a standard deviation of 14.614.6. Does this suggest that the population mean work week for men exceeds 4040 hours? Answer by completing parts (a) through (d).
Answer:
a) A. The relevant variable is the population mean work week (in hours) for workers aged 18-25.
b) Null hypothesis:[tex]\mu \leq 40[/tex]
Alternative hypothesis:[tex]\mu > 40[/tex]
c) [tex]t=\frac{45.6-40}{\frac{14.6}{\sqrt{893}}}=11.46[/tex]
The p value for this case would be:
[tex] p_v = P(t_{110} >11.46) \approx =0[/tex]
d) Since the p value is a very low value we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case exceeds 40 hours.
Step-by-step explanation:
Information provided
[tex]\bar X=45.6[/tex] represent the sample mean
[tex]s=14.6[/tex] represent the sample standard deviation
[tex]n=893[/tex] sample size
[tex]\mu_o =40[/tex] represent the value to verify
t would represent the statistic
[tex]p_v[/tex] represent the p value
a. Identify the relevant and parameter variable. Choose the correct relevant variable below.
A. The relevant variable is the population mean work week (in hours) for workers aged 18-25.
b. State the null and alternative hypotheses. State the null hypothesis.
We want to verify if the population mean is higher than 40, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 40[/tex]
Alternative hypothesis:[tex]\mu > 40[/tex]
c. Calculate the statistic
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{45.6-40}{\frac{14.6}{\sqrt{893}}}=11.46[/tex]
The p value for this case would be:
[tex] p_v = P(t_{110} >11.46) \approx =0[/tex]
d. Conclusion
Since the p value is a very low value we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case exceeds 40 hours.
